High Rate Loading Conditions Research Articles

Mixed-mode crack-tip stress intensity factors measurements by caustics method: A comparison between low and high loading rate conditions

Mixed-mode crack-tip stress field is different in low and high loading rate conditions, resulting in different mixed-mode stress intensity factors (SIFs) measurements. How to correctly measure mixed-mode SIFs in different loading rate conditions is of critical importance. To this end, mixed-mode SIFs are measured and compared by optical caustics method with high-speed photography, specifically by the interpretation of crack-tip optical image, i.e., caustics pattern which reflects crack-tip stress field. Different mixed-mode caustics patterns in shape are observed in drop weight and blast loading conditions, indicating that corresponding crack-tip stress field and mixed-mode SIFs measurements are different. Under drop weight loading, mixed-mode caustics patterns are consistent with the classical caustics interpretation for SIFs measurements, while those under reflected P wave loading in blasts are not consistent. Therefore, a modified mixed-mode caustics interpretation is proposed and verified to be available for SIFs measurements in blast loading condition. Finally, underlying reasons for different mixed-mode SIFs measurements in low and high loading rate conditions are discussed, and it is concluded that in low loading rate condition, a longer loading time results in crack-tip K-dominated stress field which is suitable for the classical caustics interpretation, while in high loading rate condition, the loading time is too short to form K-dominated stress field in the crack tip, hence a modified caustics interpretation is necessary. This paper benefits correct applications of caustics method to mixed-mode SIFs measurements in different loading rate conditions.

A transversely isotropic viscohyperelastic-damage model for the brain tissue with strain rate sensitivity

Understanding the mechanical behaviors and properties of brain tissue are crucial to study the mechanisms of traumatic brain injury (TBI). Such injury may be associated with high rate loading conditions and the large deformation of brain tissue. Thus, constitutive models that consider the rate dependent large deformation of brain tissue and its possible damage initiation and evolution may help uncover the related mechanisms of TBI. Motivated from this, in this paper we present a fully three-dimensional large strain viscohyperelastic-damage model with the purpose of reproducing the experimentally observed rate sensitive elastic and damage-induced stress softening behaviors of brain tissue. The parameters of the proposed model can be identified using the experimental data from simple monotonic tests such as uniaxial tension, compression and simple shear. The proposed model is validated by comparing its prediction with experimental data. Good agreement between predictive results and experimental data is achieved indicating the potential of the proposed model in characterizing the mechanical behaviors of brain tissue considering rate dependence and damage effect.

Residual Performance of Reinforced Concrete Beams Damaged by Low-Velocity Impact Loading

With the advancement of material science and infrastructure design technology, there is an increased need to reflect various loading scenarios in the design of civil infrastructures, including extreme loads such as impact and blast. However, structural behavior under extreme loads has been observed to be very different from that under static loads due to the high-rate loading condition. Therefore, extensive experimental and analytical studies have been conducted to explain the structural behavior under impact loading. From these efforts, various discussions have been presented on the impact behavior and the evaluation of the impact resistance of structures. However, despite the fact that the repair or reinforcement of structures damaged by impact loads is a critical issue, studies of the residual performance of impact-damaged structures are insufficient. This paper presents an experimental study to improve the understanding of the residual performance of impact-damaged structures. A total of 29 RC beams were tested under static loads to examine the effect of impact-damage on the residual behavior of RC beams. Of these, 8 RC beams were intact, and the other 21 RC beams suffered impact loading through drop weight impact tests and were damaged prior to the static flexural tests. The residual performance was evaluated by comparing the maximum load capacity, flexural stiffness, and displacement ductility of impact-damaged beams and intact beams. The comparison indicated that the flexural stiffness and displacement ductility of the impact-damaged RC beams decreased significantly, whereas their flexural strengths did not exhibit a significant difference. Predictive models for flexural stiffness and displacement ductility of the impact-damaged beams were suggested from the test results, and through these, the residual performance of the impact-damaged structure could be evaluated.

Evaluation of mode II fracture toughness under high loading rate conditions for composite bonded joints

Composite bonded joints are widely used in the aircraft components, which are frequently subjected to impact loading. The present paper intends to evaluate the mode II fracture behavior of composite bonded joints under high loading rate conditions. Dynamic loading was applied on the end-notched flexure (ENF) specimen at 10 m/s and 15 m/s via an electromagnetic split Hopkinson pressure bar system. Then the dynamic fracture toughness was evaluated using an experimental-numerical hybrid method according to the virtual crack-closure technique and compared to the fracture toughness under quasi-static loading rate (2 × 10−5 m/s and 2 × 10−4 m/s). Results indicate that the mode II fracture toughness of adhesively bonded composite joints shows a positive rate-dependent trend. The mode II fracture toughness can increase about 31.5% when the loading rate increases to 15 m/s. At last, fracture surface inspections using scanning electron microscopy (SEM) were conducted to reveal the physical mark of such an effect.

Mechanical Behavior of Multi-Material Single-Lap Joints under High Rates of Loading Using a Split Hopkinson Tension Bar

In the presented research, a split Hopkinson tension bar (SHTB) was used to measure the mechanical response of multi-material single-lap joints in the high-rate loading regime. High-performance applications require high-quality measurements of the mechanical properties to define safe design rules. Servo-hydraulic machines are commonly used to investigate such small structures, but they are prone to produce oscillation-affected force measurements. To improve force–displacement measurements, an SHTB was chosen to investigate these joints. Three different kinds of joints were tested: multi-material bolted joints, multi-material bonded joints, and multi-material bonded/bolted joints. One substrate of the joints was made of aluminum (Al-2024-T3) and the other one was made of a laminated composite (TC250). A countersunk titanium bolt and a crash-optimized epoxy adhesive (Betamate 1496 V) were used to fasten the joints. A constant impedance mounting device was implemented to limit wave reflections and to improve the signal quality. Quasi-static experiments at a servo-hydraulic machine were performed to compare the data with the respective data from the high-rate loading conditions. The presented research shows that high-quality high-rate tests of multi-material single-lap joints can be achieved by employing an SHTB. With this high-quality measurement, a rate dependency of the mechanical behavior of these joints was identified. The dynamic increase (DI), which is the ratio of a high rate of loading over quasi-static loading, was measured for each of the joint types, where the dynamic increase in the max force was DI = 1.1 for the bolted, DI = 1.4 for the bonded, and DI = 1.6 for the bonded/bolted joints.

Mode Ι fracture toughness of adhesively bonded composite joints under high loading rate conditions

ABSTRACT The purpose of this paper is to investigate the mode I fracture behavior of adhesively bonded composite joints under high loading rate conditions. A dual electromagnetic split Hopkinson pressure bar system was established to apply symmetric dynamic loading on the double cantilever beam (DCB) specimens at 15 m/s and 30 m/s. The dynamic fracture toughness was then evaluated using an experimental-numerical approach and compared to the results of quasi-static loading rate (2 × 10−5 m/s and 2 × 10−4 m/s). Results indicate that high loading rate has obvious effects on the fracture toughness of composite joints. When the loading rate increases to 30 m/s, the mode I fracture toughness can reach a value of 1645 J/m2, which is 119% higher than that of quasi-static conditions. At last, fracture surface inspections using scanning electron microscopy (SEM) were conducted to reveal such an effect.

High-rate mode II fracture toughness testing of polymer matrix composites using the Transverse Crack Tension (TCT) test

This paper describes the novel high-rate transverse crack tension (TCT) test to determine mode II fracture toughness for high strain rates and compares this to quasi-static fracture toughness obtained with the standardized End Notch Flexure (ENF) test and the modified Transverse Crack Tension (mTCT) test suggested in the literature. The novel, miniaturized mTCT specimen is used to determine the fracture toughness under quasi-static and high-rate loading conditions with an electro-mechanical test machine and a Split Hopkinson Tension bar, respectively. For the high-rate tests, almost no interfering oscillations were observed in the load signal. A novel data reduction scheme allows achieving repeatable results with a very small standard deviation. The fracture toughness for the tested composite at a loading rate of about 5 m/s was found to be at least 50% higher than the one obtained under quasi-static loading.

Dynamic crack initiation by Finite Fracture Mechanics

The development of robust failure criteria suitable for predicting crack initiation under both quasi-static and dynamic loading conditions has always garnered attention in the scientific community due to its positive impact in the trustworthiness of the failure predictions for critical structural applications. In this sense, the present work applies the well-established Finite Fracture Mechanics framework to yield failure predictions depending on the loading rate. To achieve so yet keep the analysis simple, the analogy existent between the Incubation Time dynamic failure criterion and the static formulation of the Theory of Critical Distances is herein exploited to enable the application of Finite Fracture Mechanics under certain high loading rate conditions. In particular, this is achieved by coupling the concept of incubation time to its conventional formulation.

The influence of loading rate on the ultimate capacity of bolted T-stubs at ambient and high temperature

In case of accidental actions, the robustness of multi-storey steel frame buildings depends to a large extent to the performance of the beam-to-column joints. For an extreme scenario that involves a column loss under fire, the dynamic process can induce high strain rates and therefore needs to be considered when evaluating the resistance and ductility of the beam-to-column connections. End plate bolted connections are widely used in the steel framed constructions. The simple macro-component through which the response of such a connection is assessed, consists in the T-stub model included in EN1993-1-8.The paper presents the results of an experimental program on T-stubs subjected to normal and high temperatures, in both quasi-static and high loading rate conditions. While under normal temperature the response of the T-stubs are not significantly influenced by the strain rate, at high temperatures the strain rate determines a change in the failure mode and in the ultimate resistance and deformation. The experimental study highlights the necessity of assessing the strength reduction factors of bolts function of both temperature and strain rate, a critical information in the progressive collapse assessment of structures under fire, in order to obtain realistic results.

Simulation of Dynamic Crack Initiation Based on the Peridynamic Numerical Model and the Incubation Time Criterion

Dynamic brittle fracture under high-rate loading conditions is analyzed. A new numerical algorithm based on peridynamic approach and structural–temporal model of fracture is used to predict the start of a crack in glassy polymer samples. The results of calculations are compared with available experimental data.

Acoustic emissions in vertebral cortical shell failure

Understanding the initiation of bony failure is critical in assessing the progression of bone fracture and in developing injury criteria. Detection of acoustic emissions in bone can be used to identify fractures more sensitively and at an earlier inception time compared to traditional methods. However, high rate loading conditions, complex specimen-device interaction or geometry may cause other acoustic signals. Therefore, characterization of the isolated local acoustic emission response from cortical bone fracture is essential to distinguish its characteristics from other potential acoustic sources. This work develops a technique to use acoustic emission signals to determine when cortical bone failure occurs by characterization using both a Welch power spectral density estimate and a continuous wavelet transform. Isolated cortical shell specimens from thoracic vertebral bodies with attached acoustic sensors were subjected to quasistatic loading until failure. The resulting acoustic emissions had a wideband frequency response with peaks from 20 to 900 kHz, with the spectral peaks clustered in three bands of frequencies (166 ± 52.6 kHz, 379 ± 37.2 kHz, and 668 ± 63.4 kHz). Using these frequency bands, acoustic emissions can be used as a monitoring tool in biomechanical spine testing, distinguishing bone failure from structural response. This work presents a necessary set of techniques for effectively utilizing acoustic emissions to determine the onset of cortical bone fracture in biological material testing. Acoustic signatures can be developed for other cortical bone regions of interest using the presented methods.

Spatial and Temporal Discreetness as a Crucial Property of the Dynamic Fracture Process

The paper discusses the dynamic propagation of cracks in brittle materials under various loads. The crack propagation is studied under both quasi-static and the shock-pulse loading conditions. Particular attention is paid to the dependences characterizing the crack propagation and having a non-stationary character. Thus, for the case of crack propagation under quasi-static loading, the crack velocity oscillations phenomenon is investigated. The problem related to the scatter of the stress intensity factor values which is observed in a number of experiments in course of the crack propagation under high-rate loading conditions is studied. The studies have been carried out using the finite element method with the structure–time fracture which is introduced into the computational scheme and which fundamentally determines the discrete mechanism of the fracture processes at a given scale level. Both quantitative and qualitative comparison of the calculation results with the available experimental data has been carried out. It is shown that taking into account the spatial and temporal discretization of the process makes it possible to explain a number of experimentally observed effects that do not fit into the traditional theoretical concepts of the dynamic fracture theory.

Inverse material characterisation of human aortic tissue for traumatic injury in motor vehicle crashes

Traumatic aortic rupture (TAR) resulting due to motor vehicle crashes (MVC) accounts for about 10%–20% fatalities. This article presents the outcome of our findings of the non-linear stress–strain response and strain rate-dependent behaviour of the aortic tissue under crash like impacts. This study uses both finite element (FE) modelling and experimental testing to enhance the understanding of injury mechanisms associated with TAR. Accurate material properties are essential for correct FE model predictions. Therefore, the objective of the current study was to experimentally characterise and identify a suitable constitutive model and model parameters for aortic tissue that can be incorporated into FE human body models for studying aortic rupture. Inverse characterisation and genetic algorithms (GA) were used to train the FE model to simulate real-life scenarios applying loading in multiple directions. A total of 32 uniaxial tensile tests were conducted on human aortic tissues along with the longitudinal and circumferential directions by loading at different strain rates ranging up to 200/s. The engineering stress–strain relationship obtained for human aorta in the longitudinal and circumferential directions via uniaxial tensile tests demonstrated an approximately bilinear behaviour and strain rate dependency in both directions. The higher stresses and modulus in the circumferential direction as compared to longitudinal direction demonstrates the anisotropic behaviour of the tissue. A constitutive model has been developed and implemented via user subroutine (UMAT) in LS-DYNA that accounts for the strain rate-dependent effects and bilinear behaviour observed in the aortic tissue. A FE model of the experimental set-up was developed, and the parameters of the model were estimated using a GA-based inverse mapping technique. The developed model enables investigation of the mechanical response of the aortic tissue under crashes and other high rate loading conditions. The work is based on the premise that a reliable constitutive model coupled with a FE model of the aorta shall help predict TARs.

The effect of strain rate on the orientation of the fracture plane in a unidirectional polymer matrix composite under transverse compression loading

Transverse compression tests on a unidirectional composite were performed under quasi-static and high-rate loading conditions using servo-hydraulic machines as well as a direct impact Hopkinson bar. Aside the expected increase of compressive strength with increasing loading rate, a change of fracture plane orientation was observed. For quasi-static loading conditions, the fracture angle was 54.5°, for high rate-loading conditions this increased to 65°. Assuming a Mohr-Coulomb type of fracture for unidirectional composites under transverse compression loading, the change of fracture plane orientation indicates a rate dependency of the internal friction angle ϕ, which has not previously been reported for composite materials.

Semi-Crystalline Polymers Applied to Taylor Impact Test: Constitutive, Experimental and FEM Analysis.

Based on mechanical properties of Polyamide 66 (PA66) under complex loading conditions, a Drucker–Prager yield criterion was employed to characterize its yield behavior. Then, a one-dimensional model, which contains a viscoelastic regime and a viscoplastic regime, was introduced and converted into a three-dimensional constitutive model. The three-dimensional model was implemented into a LS-DYNA software, which was used to predict the dynamic response of PA66 under Taylor impact conditions, whose corresponding tests were conducted by gas gun and recorded by high-speed camera. By contrasting the simulation results and these of the corresponding tests, the deformed shapes including the residual length, the maximum diameter and the shape of the mushroom head of the PA66 bars were found to be similar to these obtained from the tests, which verified the accuracy of the three-dimensional constitutive model, and proved that the model was able to be applied to high-rate impact loading conditions.

A calibration of the material model for FRC

This paper presents a calibration of a constitutive material model, which can be applied to describe the complex static and dynamic behavior of the fiber reinforced concrete (FRC) structures subjected to static and high-rate loading conditions. The well-known K&C material model, which is MAT072r3 as executed in LS-DYNA, is employed for the purposed of this calibration. Various experimental data on tension, compression, and high-rate behaviors of FRC material using axial and tri-axial tests are used to generate the input parameters. Numerical simulation of single specimens on compression and bending subjected to static loading, and of an FRC column under blast loading are implemented to illustrate the performance of the calibrated material model. It is shown that the calibrated material model proposed in this study presents a good agreement compared to the experimental results.

Mesomechanism of the dynamic tensile fracture and fragmentation behaviour of concrete with heterogeneous mesostructure

As a typical multi-phase material, due to its heterogeneous mesostructure, concrete exhibits complicated mechanical responses when subjected to high-rate loads. Considering concrete is much weaker in tension than in compression, it is of significance to investigate the mesomechanism of the dynamic tensile fracture behaviour of concrete under high-rate loading conditions. In this study, the meso-heterogeneity of concrete is considered by random mesostructure generation with efficient algorithm of Entrance block between A and B (E(A, B)). A 2D meso-scale model is developed by implementing a combined FDEM scheme with zero-thickness cohesive elements in ABAQUS software. The proposed model is validated by quasi-static uniaxial tension and uniaxial compression tests as well as dynamic Brazilian tensile split Hopkinson pressure bar (SHPB) test and then used in a series of Brazilian tensile SHPB tests to investigate the influences of the loading rate, aggregate area fraction and the mechanical properties of the interfacial transition zone (ITZ) on dynamic tensile behaviour of concrete. The numerical results indicate that the dynamic tensile strength increases with increasing loading rate and the fragmentation experiences a transition from parse fracturing to dramatic pulverization. A higher aggregate content has an adverse effect on the dynamic tensile strength of concrete. Moreover, the results also suggest that the mechanical properties of the ITZ play a significant role on the dynamic tensile behaviour of concrete.

Mode I stress intensity factors measurements in PMMA by caustics method: A comparison between low and high loading rate conditions

Caustics method has been widely used in dynamic stress intensity factors (DSIFs) measurements in PMMA by the size of caustics patterns. However, caustics geometry may be different between low and high loading rate conditions. To make data interpretation of caustics method as precise as possible, in this paper, mode I crack propagation under drop weight and blast stress wave loadings were investigated by caustics method with high-speed photography. It was found that approximate circle caustics patterns occurred under drop weight loading, while ellipse caustics patterns appeared under blast stress wave loading. These caustics patterns with different geometry were recreated by mathematical simulation, and then a new relationship between DSIFs and diameters of caustics patterns was built for precise DSIFs measurements. Finally, optical microscopic view of fracture surfaces shown that circle and ellipse caustics patterns corresponded to smooth and rough fracture surfaces, respectively. This paper indicates that caustics geometry and fracture surface roughness are important considerations when measuring DSIFs by caustics method in high loading rate conditions, otherwise large errors may occur.

Determination of the strain-energy release rate of a composite laminate under high-rate tensile deformation in fibre direction

In order to successfully model design-critical impact loading events on laminated composite structures, the rate-dependency of the composite material has to be correctly reflected. In this context, the rate-dependency of the strain-energy release rate for fibre tensile failure under high-rate loading conditions has not yet been satisfyingly explored. This study employed compact tension specimens consisting of IM7/8552 for dynamic testing on a split-Hopkinson tension bar system. Data reduction was based on the area method. The obtained strain-energy release rate for testing under high-rate conditions was determined to GIc,dynf+=82.0±20.8kJ/m2, exhibiting a salient drop compared to its counterpart obtained under quasi-static loading (GIc,QSf+=195.8±18.0kJ/m2). Analysis of the strain field surrounding the crack tip using digital image correlation (DIC) suggested a more extensive damage zone for testing under quasi-static than for high-rate loading. A fractographic analysis of the specimens did not indicate any pronounced difference in terms of fracture surface morphology across the two loading rate regimes.

A methodology for the generation and non-destructive characterisation of transverse fractures in long bones

Long bone fractures are common and although treatments are highly effective in most cases, it is challenging to achieve successful repair for groups such as open and periprosthetic fractures. Previous biomechanical studies of fracture repair, including computer and experimental models, have simplified the fracture with a flat geometry or a gap, and there is a need for a more accurate fracture representation to mimic the situation in-vivo. The aims of this study were to develop a methodology for generating repeatable transverse fractures in long bones in-vitro and to characterise the fracture surface using non-invasive computer tomography (CT) methods. Ten porcine femora were fractured in a custom-built rig under high-rate loading conditions to generate consistent transverse fractures (angle to femoral axis < 30 degrees). The bones were imaged using high resolution peripheral quantitative CT (HR-pQCT). A method was developed to extract the roughness and form profiles of the fracture surface from the image data using custom code and Guassian filters. The method was tested and validated using artificially generated waveforms. The results revealed that the smoothing algorithm used in the script was robust but the optimum kernel size has to be considered.